(Forgive me if this software has already been mentioned in this thread.)
After numerous Google and Droid forum searches, and several unsuccessful attempts using Handbrake, I finally found what I was looking for: DVD Catalyst Free.
The full version is very reasonable at the price of $10, but the free version is fine for me at this point. It detects and scans the DVD in my computer, I can name the file and choose where it will be sent after ripping, and I can select my device from a drop-down list. I used the USB cable to transfer the MPEG4 file to my Droid Eris, and it the movie plays fine with the stock player.
I don't need tons of customizable options, which are available in the paid full version. I highly recommend DVD Catalyst! (And I am in no way affiliated with the programmer, developer, or website!) There is also a limited trial version available for download.
Check it out at Tools4Movies, Official home of DVD Catalyst